What are the quartiles for the given dataset? 115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
To find the quartiles for the given dataset, we need to first arrange the data in ascending order:
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
The median of the entire dataset is the value that divides the dataset into two equal halves. Since there are 13 values in the dataset, the median is the average of the 6th and 7th values, which are both 125. Therefore, Q2 (the second quartile, also known as the median) is 125.
To find Q1 (the first quartile), we need to find the median of the lower half of the dataset. The lower half of the dataset consists of the values below the median, which are:
115, 117, 120, 122
The median of this lower half is the average of the 2nd and 3rd values, which are 117 and 120. Therefore, Q1 is 118.5 (the average of 117 and 120).
To find Q3 (the third quartile), we need to find the median of the upper half of the dataset. The upper half of the dataset consists of the values above the median, which are:
127, 128, 131, 132, 136, 136, 140
The median of this upper half is the average of the 4th and 5th values, which are 132 and 136. Therefore, Q3 is 134 (the average of 132 and 136).
To find the quartiles for the given dataset, follow these steps:
Step 1: Sort the dataset in ascending order:
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
Step 2: Calculate the median (Q2), which is the middle value of the dataset:
Median (Q2) = (125 + 127) / 2 = 126
Step 3: Divide the dataset into two halves. For the lower half, find the median (Q1) of the values below the median:
115, 117, 120, 122, 125
Q1 = (117 + 120) / 2 = 118.5
Step 4: Find the median (Q3) of the upper half of the dataset, which is the values above the median:
127, 128, 131, 132, 136, 136, 140
Q3 = (131 + 132) / 2 = 131.5
Therefore, the quartiles for the given dataset are:
Q1 = 118.5
Q2 = 126
Q3 = 131.5